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version 1.14, 2016/08/27 15:34:49
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*> \brief \b ZHBGV |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZHBGV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgv.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgv.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgv.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, |
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* LDZ, WORK, RWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER JOBZ, UPLO |
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* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION RWORK( * ), W( * ) |
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* COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), |
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* $ Z( LDZ, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors |
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*> of a complex generalized Hermitian-definite banded eigenproblem, of |
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*> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian |
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*> and banded, and B is also positive definite. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] JOBZ |
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*> \verbatim |
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*> JOBZ is CHARACTER*1 |
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*> = 'N': Compute eigenvalues only; |
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*> = 'V': Compute eigenvalues and eigenvectors. |
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*> \endverbatim |
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*> |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangles of A and B are stored; |
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*> = 'L': Lower triangles of A and B are stored. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrices A and B. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KA |
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*> \verbatim |
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*> KA is INTEGER |
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*> The number of superdiagonals of the matrix A if UPLO = 'U', |
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*> or the number of subdiagonals if UPLO = 'L'. KA >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KB |
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*> \verbatim |
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*> KB is INTEGER |
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*> The number of superdiagonals of the matrix B if UPLO = 'U', |
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*> or the number of subdiagonals if UPLO = 'L'. KB >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AB |
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*> \verbatim |
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*> AB is COMPLEX*16 array, dimension (LDAB, N) |
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*> On entry, the upper or lower triangle of the Hermitian band |
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*> matrix A, stored in the first ka+1 rows of the array. The |
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*> j-th column of A is stored in the j-th column of the array AB |
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*> as follows: |
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*> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; |
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). |
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*> |
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*> On exit, the contents of AB are destroyed. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> The leading dimension of the array AB. LDAB >= KA+1. |
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*> \endverbatim |
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*> |
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*> \param[in,out] BB |
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*> \verbatim |
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*> BB is COMPLEX*16 array, dimension (LDBB, N) |
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*> On entry, the upper or lower triangle of the Hermitian band |
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*> matrix B, stored in the first kb+1 rows of the array. The |
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*> j-th column of B is stored in the j-th column of the array BB |
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*> as follows: |
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*> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; |
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*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). |
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*> |
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*> On exit, the factor S from the split Cholesky factorization |
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*> B = S**H*S, as returned by ZPBSTF. |
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*> \endverbatim |
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*> |
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*> \param[in] LDBB |
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*> \verbatim |
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*> LDBB is INTEGER |
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*> The leading dimension of the array BB. LDBB >= KB+1. |
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*> \endverbatim |
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*> |
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*> \param[out] W |
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*> \verbatim |
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*> W is DOUBLE PRECISION array, dimension (N) |
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*> If INFO = 0, the eigenvalues in ascending order. |
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*> \endverbatim |
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*> |
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*> \param[out] Z |
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*> \verbatim |
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*> Z is COMPLEX*16 array, dimension (LDZ, N) |
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*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of |
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*> eigenvectors, with the i-th column of Z holding the |
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*> eigenvector associated with W(i). The eigenvectors are |
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*> normalized so that Z**H*B*Z = I. |
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*> If JOBZ = 'N', then Z is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDZ |
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*> \verbatim |
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*> LDZ is INTEGER |
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*> The leading dimension of the array Z. LDZ >= 1, and if |
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*> JOBZ = 'V', LDZ >= N. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (N) |
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*> \endverbatim |
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*> |
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*> \param[out] RWORK |
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*> \verbatim |
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*> RWORK is DOUBLE PRECISION array, dimension (3*N) |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, and i is: |
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*> <= N: the algorithm failed to converge: |
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*> i off-diagonal elements of an intermediate |
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*> tridiagonal form did not converge to zero; |
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*> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF |
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*> returned INFO = i: B is not positive definite. |
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*> The factorization of B could not be completed and |
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*> no eigenvalues or eigenvectors were computed. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2015 |
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* |
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*> \ingroup complex16OTHEReigen |
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* |
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* ===================================================================== |
SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, |
SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, |
$ LDZ, WORK, RWORK, INFO ) |
$ LDZ, WORK, RWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.6.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2015 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
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$ Z( LDZ, * ) |
$ Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZHBGV computes all the eigenvalues, and optionally, the eigenvectors |
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* of a complex generalized Hermitian-definite banded eigenproblem, of |
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* the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian |
|
* and banded, and B is also positive definite. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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* JOBZ (input) CHARACTER*1 |
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* = 'N': Compute eigenvalues only; |
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* = 'V': Compute eigenvalues and eigenvectors. |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangles of A and B are stored; |
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* = 'L': Lower triangles of A and B are stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrices A and B. N >= 0. |
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* |
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* KA (input) INTEGER |
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* The number of superdiagonals of the matrix A if UPLO = 'U', |
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* or the number of subdiagonals if UPLO = 'L'. KA >= 0. |
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* |
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* KB (input) INTEGER |
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* The number of superdiagonals of the matrix B if UPLO = 'U', |
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* or the number of subdiagonals if UPLO = 'L'. KB >= 0. |
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* |
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* AB (input/output) COMPLEX*16 array, dimension (LDAB, N) |
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* On entry, the upper or lower triangle of the Hermitian band |
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* matrix A, stored in the first ka+1 rows of the array. The |
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* j-th column of A is stored in the j-th column of the array AB |
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* as follows: |
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* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; |
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). |
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* |
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* On exit, the contents of AB are destroyed. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KA+1. |
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* |
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* BB (input/output) COMPLEX*16 array, dimension (LDBB, N) |
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* On entry, the upper or lower triangle of the Hermitian band |
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* matrix B, stored in the first kb+1 rows of the array. The |
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* j-th column of B is stored in the j-th column of the array BB |
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* as follows: |
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* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; |
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* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). |
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* |
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* On exit, the factor S from the split Cholesky factorization |
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* B = S**H*S, as returned by ZPBSTF. |
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* |
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* LDBB (input) INTEGER |
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* The leading dimension of the array BB. LDBB >= KB+1. |
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* |
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* W (output) DOUBLE PRECISION array, dimension (N) |
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* If INFO = 0, the eigenvalues in ascending order. |
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* |
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* Z (output) COMPLEX*16 array, dimension (LDZ, N) |
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* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of |
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* eigenvectors, with the i-th column of Z holding the |
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* eigenvector associated with W(i). The eigenvectors are |
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* normalized so that Z**H*B*Z = I. |
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* If JOBZ = 'N', then Z is not referenced. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1, and if |
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* JOBZ = 'V', LDZ >= N. |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (N) |
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* |
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* RWORK (workspace) DOUBLE PRECISION array, dimension (3*N) |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = i, and i is: |
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* <= N: the algorithm failed to converge: |
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* i off-diagonal elements of an intermediate |
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* tridiagonal form did not converge to zero; |
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* > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF |
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* returned INFO = i: B is not positive definite. |
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* The factorization of B could not be completed and |
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* no eigenvalues or eigenvectors were computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |